Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #23367 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C23×D7 |
| commutator, socle, prime radical | C23×C7 | C23×C4 |
| Fitting | C7×#2399 | C2 |
| cosocle | C22×C4×C7 | C24 |
| hypercenter | #2399 | D7 |
| hypocenter | C7 | #23367 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C22×C4 ◁ #2399 | |
600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1792 |
Polycyclic presentation:
2^8,7|a^2=g,b^2=e,c^2=ef,d^2=e,g^2=h,b^a=be,c^a=cf,d^a=def,i^a=i^6,c^b=cef,d^b=de,d^c=dh196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 196184);